id: 06539008
dt: j
an: 2016b.00261
au: Dowling, Paul
ti: Social activity method: a fractal language for mathematics.
so: Philos. Math. Educ. J. 29, 23 p., electronic only (2015).
py: 2015
pu: Professor Paul Ernest, University of Exeter, Graduate School of Education,
Exeter
la: EN
cc: D20 E20 E40 D50
ut: mathematics and philosophy; sociology; social activity method; discursive
saturation; grammatical modes; organisational languages; internal
language; external language; domains of action; forensic relation;
relation of constructive description; modes of recontextualisation;
mathematics and the esoteric domain; mathematics and language; problem
posing
ci:
li: http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome29/Paul%20Dowling%20%20Social%20Activity%20Method.docx
ab: Summary: In this paper I shall present and develop my organisational
language, “social activity method" (SAM) and illustrate some of its
applications. I shall introduce a new scheme for “modes of
recontextualisation" that enables the analysis of the ways in which one
activity ‒ which might be school mathematics or social research or
any empirically observed regularity of practice ‒ recontextualises
the practice of another and I shall also present, deploy and develop an
existing scheme ‒ “domains of action" ‒ in an analysis of school
mathematics examination papers and in the structuring of what I refer
to as the “esoteric domain". This domain is here conceived as a
hybrid domain of, firstly, linguistic and extralinguistic resources
that are unambiguously mathematical in terms of both expression and
content and, secondly, pedagogic theory ‒ often tacit ‒ that
enables the mathematical gaze onto other practices and so
recontextualises them. A second and more general theme that runs
through the paper is the claim that there is nothing that is beyond
semiosis, that there is nothing to which we have direct access,
unmediated by interpretation. This state of affairs has implications
for mathematics education. Specifically, insofar as an individual’s
mathematical semiotic system is under continuous development ‒ the
curriculum never being graspable all at once ‒ understanding ‒ as a
stable semiotic moment ‒ of any aspect or object of mathematics is
always localised to the individual and is at best transient and the
sequencing of such moments may well also be more individualised than
consistent in some correspondence with the sequencing of the
curriculum. This being the case, a concentration on understanding as a
goal may well serve to inhibit the pragmatic acquisition and deployment
of mathematical technologies, which should be the principal aim of
mathematics teaching and learning. The paper is primarily concerned
with mathematics education. SAM, however, is a language that is
available for recruiting and deploying in potentially any context as I
have attempted to illustrate with some of the secondary illustrations
in the text.
rv: